HL11-1.ppt Objectives 11.1.1 & 11.1.2 Introduction to Uncertainty
Learning Objectives • 11.1.1 • Describe and give examples of random uncertainties and systematic errors • 11.1.2 • Distinguish between precision and accuracy. • It is possible for a measurement to have great precision yet be inaccurate (for example, if the top of a meniscus is read in a pipette or measuring cylinder)
Learning Objectives 11.1.3 Describe how the effects of random uncertainties may be reduced. 11.1.4 State random uncertainty as an uncertainty range. 11.1.5 State the results of calculations to the appropriate number of significant figures.
Qualitative vs. Quantitative Measurements • What’s the difference? • Give an example of each. • IB expects you to address both when writing labs. • We are going to focus on quantitative measurements in this unit.
Experimental Errors • Where do these errors and thus the uncertainty come from? • Sources: • Imperfect or inappropriate measuring tools (Random Uncertainties) • Hurried or unskilled measurers (Systematic Errors) • Poorly designed procedures (Systematic Errors)
Random Uncertainties • Make measurements LESS precise • Are usually due to inadequacies or limitations in your measuring instruments
Making Measurements on Analog Devices • Remember that the measuring tool determines how accurate a measurement can be. • What would be the correct measurement here?
1.4 - Review of Uncertainty in Measurements • YOU MUST ESTIMATE TO 0.1 OF THE SMALLEST GRADATION ON A MEASURING DEVICE. • 53 ml is not enough precision here. • 52.8 ml would be better. • Including the uncertainty factor we should record this measurement as 52.8 ± 0.5 mL
Dealing with Uncertainty • Uncertainty is denoted with a ± value. • The ± value is an estimation of the uncertainty. • Often it is given to you by the manufacturer of the measuring tool. • If not, we generally take the uncertainty to be ± 1/2 of the value of the smallest increment on the tool. • What do you think would be your uncertainty in this case?
Dealing with Uncertainty • What do you think your precision (uncertainty) would be in this case? • ± 0.05oC [Caution – sometimes digital outputs can be misleading. The documentation for this thermometer actually indicates that it can only accurately read ± 0.2oC. In this case, the uncertainty of the equipment is limited by its accuracy. You would report the uncertainty as ± 0.2oC, not the estimate of ± 0.05oC.
Dealing with Inaccuracy • Would it be possible to be very precise with this measurement yet be inaccurate? • We measure the accuracy of measurements with percentage error. • What is the formula for percentage deviation? • % Dev=|(Exp-Acc)/Acc|
Systematic Errors • Always affect the result in a particular direction. • from flaws in the measuring device or poor technique in using the device • from a procedure with poorly controlled variables. • Which illustration shows an obvious systematic error? • Think of a scenario in a lab that would result in a systematic error.
Significant Figures • All certain digits plus one uncertain digit. • Be able to count sig figs and to do routine calculations with them… rounding the answer to the appropriate number of sig figs. • See gold sheet for specifics.
HW – Do the Text Assignment for 11.1 (Due Friday) • See your Ch. 11 objectives